Hosting a Facebook Application?
I have looked on FaceBook Developer page and found that it's possible to create a FaceBook application, however this application must be hosted by you!
I'm new, does any one have an experience on that?
I don't really see a question. Surely a lot developers created such an application (see all the available apps in facebook).
I personally tried it once. And yes, you need a place to publish your aplication (webserver)...
Some help to start: https://developers.facebook.com/docs/
Yes, you have to have a server external to Facebook. Basically what happens is you give facebook the URL to your application. When someone tries to view it from facebook (http://app.facebook.com/yourAppName/) it will forward the request, along with some special keys for validation, to your application's server. All your code is on your hosting server, and from there is can make calls back to facebook's API/web services to get any needed data. Then you can return any UI/HTML/FBML markup in the reply, and facebook will display it.
There are a bunch of prewritten libraries for Facebook too, for several languages. For example, Facebooker for Ruby.